Regularized covariance estimation in scaled Gaussian models

Ami Wiesel*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations

Abstract

We consider regularized covariance estimation in scaled Gaussian settings, e.g., Elliptical distributions, compound-Gaussian processes and spherically invariant random vectors. The classical maximum likelihood (ML) estimate due to Tyler is asymptotically optimal under different criteria and can be efficiently computed even though the optimization is non-convex. We propose a unified framework for regularizing this estimate in order to improve its finite sample performance. Our approach is based on the discovery of hidden convexity within the ML objective, namely convexity on the manifold of positive definite matrices. We regularize the problem using appropriately convex penalties. These allow for shrinkage towards the identity matrix, shrinkage towards a diagonal matrix, shrinkage towards a given positive definite matrix, and regularization of the condition number. We demonstrate the advantages of these estimators using numerical simulations.

Original languageEnglish
Title of host publication2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2011
Pages309-312
Number of pages4
DOIs
StatePublished - 2011
Event2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2011 - San Juan, Puerto Rico
Duration: 13 Dec 201116 Dec 2011

Publication series

Name2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2011

Conference

Conference2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2011
Country/TerritoryPuerto Rico
CitySan Juan
Period13/12/1116/12/11

Keywords

  • Covariance estimation
  • hidden convexity
  • optimization on manifolds
  • regularization
  • robust statistics

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